A Dialectical Approach to the Formation of Mathematical Abstractions

Autor/inn/en	Ozmantar, Mehmet Fatih; Monaghan, John
Titel	A Dialectical Approach to the Formation of Mathematical Abstractions
Quelle	In: Mathematics Education Research Journal, 19 (2007) 2, S.89-112 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1033-2170
Schlagwörter	Tutors; Abstract Reasoning; Student Development; Models; Mathematics Instruction; Mathematics Skills; Skill Development; Cognitive Processes; Algebra; National Curriculum; Foreign Countries; Scaffolding (Teaching Technique); Graphs; Turkey + Suchen Sie Ihr Suchwort? Förderlehrer; Lehrender; Tutor; Abstraktes Denken; Denken; Analogiemodell; Mathematics lessons; Mathematikunterricht; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Kompetenzentwicklung; Qualifikationsentwicklung; Cognitive process; Kognitiver Prozess; Ausland; Grafische Darstellung; Türkei
Abstract	This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in context. This model constitutes the basis of the second section where we describe an empirical study designed to investigate mathematical abstraction in socially rich (e.g., peer-interacted and tutor-assisted) environments. We then present data on two students working with the help of a tutor on tasks concerned with graphs of absolute value functions. On the basis of these data, we discuss four particular themes which are relevant to the purpose of this special issue and are important in the discussion of mathematical abstraction: human and artefact mediation, tutor interventions in assisting the formation of mathematical abstractions, implications of a dialectical view on student development, and the things that are abstracted. (Contains 1 footnote and 2 figures.) (Author).
Anmerkungen	Mathematics Education Research Group of Australasia. MERGA-GPO Box 2747, Adelaide, South Australia 5001, Australia. Web Site: http://www.merga.net.au/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10